OBJ: Solve Linear systems graphically

1
OBJ Solve Linear systems graphically
algebraically
IN YOUR NOTEBOOK.

• Do Now Solve GRAPHICALLY
• 1) y 2x 4
• y x - 1

• Do Now Solve ALGEBRAICALLY
• Substitution OR Linear Combination
• 2) 2x 3y 5
• 2x y 4

2
3.6 Solving Systems of Linear Equations in Three
Variables

• CHOOSE THE SAME VARIABLE TO ELIMINATE FROM EACH
  SET EQN 12 THEN EQN 23
• SOLVE AGAIN BUT USING THE NEW EQNS THIS TIME
• SUBSTITUTE TO FIND THE LAST VARIABLE

3
Ex

• 3x 2y 4z 11
• 2x y 3z 4
• 5x 3y 5z -1
• FIND WHICH VARIABLE YOU CAN ELIMINATE FROM EQN
  1 2 AND
• EQN 2 3

4

• LETS PICK TO ELIMINATE y
• 3x 2y 4z 11
• 2x y 3z 4

5

• SINCE YOU ELIMINATED y
• YOU NEED TO ELIMINATE THE SAME VARIABLE AGAIN
  NOW
• 2x y 3z 4
• 5x 3y 5z -1

6

• SOLVE THE NEW EQUATIONS
• FROM EQN 12 7x 10z 19
• FROM EQN 23 -x 4z -13

7

• SUBSTITUTE BACK INTO ANY OF THE ORIGINAL
  EQUATIONS TO FIND THE REMAINING VARIABLE
• 3x 2y 4z 11

8

• WRITE THE SOLUTION AS AN ORDERED TRIPLE
• (-3, 2, 4)